I actually think Cora has been a big influence in the recent changes that the team has made regarding analytics. Yes, Dombrowski hired Cora, for which I gave him kudos. However, he also turned right around and hired LaRussa, which says to me that while he's willing to give the new school a look, he's not fully on board with it.
I cannot imagine that he is spearheading the move to greater use of analytics. He's willing to go along with the suggestions, etc., but he's not initiating these moves.